Information on Result #1235238
Linear OOA(3199, large, F3, 5, 11), using extracting embedded OOA based on digital (188, 199, large)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (41, 46, 4194301)-net over F3, using
- net defined by OOA [i] based on linear OOA(346, 4194301, F3, 5, 5) (dual of [(4194301, 5), 20971459, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(346, large, F3, 5) (dual of [large, large−46, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(346, large, F3, 5) (dual of [large, large−46, 6]-code), using
- net defined by OOA [i] based on linear OOA(346, 4194301, F3, 5, 5) (dual of [(4194301, 5), 20971459, 6]-NRT-code), using
- digital (142, 153, 5033160)-net over F3, using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F27, using
- net defined by OOA [i] based on linear OOA(2751, 1677720, F27, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2751, 8388601, F27, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2751, large, F27, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2751, large, F27, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2751, 8388601, F27, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(2751, 1677720, F27, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F27, using
- digital (41, 46, 4194301)-net over F3, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3199, large, F3, 5, 10) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3199, large, F3, 5, 9) | [i] | ||
| 3 | Linear OOA(3199, large, F3, 5, 8) | [i] | ||
| 4 | Linear OOA(3199, large, F3, 5, 7) | [i] | ||
| 5 | Linear OOA(3199, large, F3, 5, 6) | [i] | ||
| 6 | Linear OOA(3199, large, F3, 5, 5) | [i] | ||
| 7 | Linear OOA(3199, large, F3, 5, 4) | [i] | ||
| 8 | Linear OOA(3199, large, F3, 5, 3) | [i] | ||
| 9 | Linear OOA(3204, large, F3, 5, 11) | [i] | NRT-Code Embedding in Larger Space | |
| 10 | Linear OOA(3209, large, F3, 5, 11) | [i] | ||
| 11 | Linear OOA(3214, large, F3, 5, 11) | [i] | ||
| 12 | Linear OOA(3219, large, F3, 5, 11) | [i] | ||
| 13 | Linear OOA(3224, large, F3, 5, 11) | [i] | ||
| 14 | Linear OOA(3229, large, F3, 5, 11) | [i] | ||
| 15 | Linear OOA(3234, large, F3, 5, 11) | [i] | ||
| 16 | Linear OOA(3239, large, F3, 5, 11) | [i] | ||
| 17 | Linear OOA(3244, large, F3, 5, 11) | [i] | ||
| 18 | Linear OOA(3249, large, F3, 5, 11) | [i] | ||
| 19 | Linear OOA(3200, large, F3, 5, 11) | [i] | OOA Duplication | |
| 20 | Linear OOA(3201, large, F3, 5, 11) | [i] | ||
| 21 | Linear OOA(3202, large, F3, 5, 11) | [i] | ||
| 22 | Linear OOA(3203, large, F3, 5, 11) | [i] | ||